Some embodiments described herein relate generally to outputting asset values, and more particularly to methods and apparatus for determining and outputting price and transaction values for an index multiplier fund.
Many known accounting systems are limited to a single model for establishing the value (V) of an asset: price times quantity (P*Q). While this model is broadly applicable and effective, it fails to account for additional complexity inherent in many real-world asset valuation methods. For example, the value of produce is a function not only of price times quantity, but also of time. Because fruit is often picked before it is ripe, its price may increase over time as it ripens. Thus, the value of a given amount of fruit is better expressed using a modified P*Q model, where P=F(t), and t is the variable time. In this example, the pricing value function F(t) starts low, rises over time to peak ripeness, then declines to zero as the value of the produce declines to a complete write-off as spoilage occurs. Thus, a more-accurate valuation model for fruit can be expressed as V=F(t) Q, where F(t) is the unit price of the fruit at a given time t (with the quantity of fruit, Q, being constant throughout the maturation process).
In addition, the value of some assets can change as a function of value-add that takes place during the production, manufacturing and/or distribution processes. These processes can also alter the quantity of the asset. For example, the value of the inventory of a lumber mill may increase, and the quantity decrease, as lumber is transformed from board feet to finished roof trusses or moldings. Thus, in an appropriate modified P*Q model, price (P)=F(stage) and quantity (Q)=F2(stage), where stage represents a step function related to the stage in the transformation of the lumber into the finished product. Typically, in this processing, P increases from stage to stage, while Q decreases or has its metric completely transformed (e.g., from board feet to linear feet for a molding). Using this modified method of determining P and Q, a modified valuation model for lumber can be expressed V=F(stage)*F2(stage).
In investing, the growth of index funds (such as Exchange Traded Funds, or “ETFs”) has been followed by an expansion in aggressive, leveraged funds based on an underlying index fund. The daily change in price of these “multiplier funds” is a multiple of the daily percentage change of the underlying index on which the multiplier fund is based. While on an intra-day and daily basis these multiplier funds closely mirror the performance of the underlying index, the nature of the P*Q pricing mechanism causes such funds to lose fidelity with the underlying index over time. This loss of fidelity is caused by the natural changes in direction (e.g., from rising to falling or vice-versa) in the daily closing value of the underlying index, which create a divergence between the multiplier fund and the underlying index. This divergence means that an investor may incur a loss in the sale of a multiplier fund even though its underlying index is equal to or higher than the value point at which the multiplier fund was purchased. Over time these daily index fluctuations manifest multiple changes in “direction” (i.e., from gain to loss or loss to gain), which can cause this performance gap to continually grow. While many investors in aggressive multiplier funds are day-traders who remain unaffected by this divergence (since it only arises over time), such funds can impose a significant penalty on positions taken over a longer duration.
Thus, a standard two-variable P*Q value model for a multiplier fund does not provide sufficient degrees of freedom to track the value of produce over time, to track the value of inputs being transformed, or to both accurately track daily percentage changes in an underlying index fund and maintain fidelity therewith. As such, a need exists for methods and apparatus that utilize a multi-variable method to value a multiplier fund, thereby exploiting its inherent aggressiveness without incurring the above-described performance gap. These methods can also be applied to other valuation problems such as produce and milled lumber in order to provide current dynamic inventory, rather than a periodic (e.g., quarterly) estimate or hard count.